Solve 1/4x-1/3<x+2

$$\frac { 1 } { 4 } x - \frac { 1 } { 3 } < x + 2$$

Solve for x

$$x>-\frac{28}{9}$$

Solution Steps

Subtract x from both sides.

$$\frac{1}{4}x-\frac{1}{3}-x<2$$

Combine \frac{1}{4}x and -x to get -\frac{3}{4}x.

$$-\frac{3}{4}x-\frac{1}{3}<2$$

Add \frac{1}{3} to both sides.

$$-\frac{3}{4}x<2+\frac{1}{3}$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{3}{4}x<\frac{6}{3}+\frac{1}{3}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$-\frac{3}{4}x<\frac{6+1}{3}$$

Add 6 and 1 to get 7.

$$-\frac{3}{4}x<\frac{7}{3}$$

Multiply both sides by -\frac{4}{3}, the reciprocal of -\frac{3}{4}. Since -\frac{3}{4} is negative, the inequality direction is changed.

$$x>\frac{7}{3}\left(-\frac{4}{3}\right)$$

Multiply \frac{7}{3} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{7\left(-4\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{7\left(-4\right)}{3\times 3}.

$$x>\frac{-28}{9}$$

Fraction \frac{-28}{9} can be rewritten as -\frac{28}{9} by extracting the negative sign.

$$x>-\frac{28}{9}$$